CARBON
4 7 ( 2 0 0 9 ) 2 8 9 8 –2 9 0 3
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/carbon
Enhanced optical absorption cross-section characteristics
of multi-wall carbon nanotubes
C. Ni, P.R. Bandaru*
Materials Science Program, Department of Mechanical and Aerospace Engineering, University of California, San Diego, Room 258, Engineering
2, 9500 Gilman Drive, MC 0411, La Jolla, CA 92093-0411, United States
A R T I C L E I N F O
A B S T R A C T
Article history:
The optical absorption anisotropy of multi-walled carbon nanotubes (MWCNTs) has been
Received 2 March 2009
quantitatively characterized through the determination of the absorbance and the degree
Accepted 15 June 2009
of linear polarization. A model considering the orientation of the MWCNTs and the sensi-
Available online 21 June 2009
tivity to both co-polarized and cross-polarized radiation, through electric field depolarization effects, was used to understand the experimental results. The MWCNT optical
absorption cross-sections for both the co-polarized radiation (0.1 Å2/atom) and the
cross-polarized radiation (0.05 Å2/atom) were found to be much larger than for singlewalled carbon nanotubes. Our results indicate the promise of MWCNTs for applications
involving radiation absorption.
2009 Elsevier Ltd. All rights reserved.
1.
Introduction
The optical properties of both single-walled and multi-walled
carbon nanotubes (CNTs) have been intensively studied for
many applications [1] incorporating light emission [2], detection [3], and a wide electromagnetic absorption spectrum (60–
2500 nm) [4–6]. The additional combination of high mechanical
strength [7] together with appreciable electronic [8] and thermal conductivity [8,9] could also enable CNTs for coating materials, e.g., in pyroelectric detectors [10] and solar energy
conversion.
A defining characteristic of the optical properties of CNTs
arises from their anisotropic absorption due to their large aspect ratio/quasi one-dimensional topology. For example, it
was seen that the absorption of electromagnetic radiation
polarized parallel (co-/p-polarized) to the nanotube axis is larger than for the radiation polarized perpendicular (cross-/spolarized) to the axis [11,12]. Such anisotropy can be quantitatively understood through the measurement of the optical
absorption cross-section (r), which is related to the ratio of
the transmitted intensity (I) to the incident intensity (I0),
through I = I0 exp(nrt) for a certain thickness (t) of the material and material/CNT density (n). Note that the absorption
coefficient is defined here as nr, while the absorbance, K, is
nrt. The transmittance (T) is defined and measured through I/I0.
In this paper, we report on the optical absorption cross-section anisotropy (r||/r?; r|| for co-polarization and r? for crosspolarization) for multi-walled CNTs (MWCNTs) as a function
of nanotube diameter. Such measurements and quantitative
determination, in addition to being of scientific interest, can
be used to interpret the degree of CNT alignment [12]. It was
seen that in comparison to the single-walled CNTs (SWCNTs)
[12], MWCNTs have much higher absorption cross-sections
[13] with a dominant contribution from the outermost layers.
2.
Experimental procedure
Mats comprising vertically aligned MWCNTs were synthesized on quartz substrates via thermal chemical vapor deposition (CVD), using a 2–7 nm thick electron-beam evaporated
Fe catalyst film. The CNT growth was carried out using a mixture of C2H2 (99.96%) and Ar (99.999%) with flow rates of
* Corresponding author: Fax: +1 858 534 5698.
E-mail address: [email protected] (P.R. Bandaru).
0008-6223/$ - see front matter 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.carbon.2009.06.038
CARBON
4 7 ( 20 0 9 ) 2 8 9 8–29 0 3
2899
Fig. 1 – (a) SEM and (b) TEM images of synthesized MWCNT ensembles, (c) schematic of experimental setup of the absorption
measurements, in the (d) co-polarized, and (e) cross-polarized configurations.
30 sccm and 400 sccm, respectively. SEM images of the nanotube film revealed a uniformly aligned MWCNT ensemble
(Fig. 1a) with an average height, L 15 lm, and diameter in
the range of 5–20 nm (Fig. 1a).
The optical characterization was implemented mainly
through the experimental setup illustrated in Fig. 1c. Polarized light (473 nm/633 nm) from linearly polarized lasers
was shone onto the MWCNT sample (at an angle h; 0 < h < p/
2). The optical path length, t, is hence equal to L/(cos h). The
measurements were conducted both in the co-polarized (electric field parallel to the plane of incidence (Fig. 1d) – and
cross-polarized (electric field perpendicular to the plane of incidence (Fig. 1e) – configurations. The transmitted intensity was
analyzed by a polarizer, before being collected by a photodetector (Thorlabs DET 110).
3.
Results and discussion
3.1.
Absorbance characteristics of MWCNTs
Fig. 2a shows the measured transmitted intensity (I) dependence of the MWCNT samples for co- and cross-polarized radi-
ation of wavelengths 473 and 633 nm as a function of
substrate tilt, h. In the figure caption, we use arbitrary units
for I as neutral density filters were used (to bring the signals
to the measurable range of the lock-in amplifier). A higher
transmission was observed for the cross-polarized radiation
compared to the co-polarized case, due to electric-field-induced depolarization from the nanotube cross-section in the
latter which reduces the dynamical conductivity and lowers
optical absorption [14]. A reduced transmission for shorter
wavelength radiation was also noted [12,13] and could arise
from increased propensity for surface and bulk p-plasmon
excitations [15]. The absorbance (K) was calculated from the
ratio of the transmitted to the incident intensity, through
I = I0 exp(K), and is plotted in Fig. 2b. The effective thickness,
t, in K (=nrt) was normalized to t = L/cos h, to account for the
substrate tilt. While in the cross-polarized case, the absorbance, Kcr, was largely independent of h – as expected from
Fig. 1d, a sin2 h variation for the co-polarized absorbance, Kco
(Fig. 2c) was observed. It was noted that the Kco for 473 nm
was lower at larger h, compared to the 633 nm case, due to
greater light leakage. Such a dependence was justified when
the component of the electric field parallel to the nanotube,
2900
CARBON
4 7 ( 2 0 0 9 ) 2 8 9 8 –2 9 0 3
Fig. 2 – (a) Transmitted intensity of 633 and 473-nm radiation for the co- (co-) and cross- (cr-) polarized configurations. (b) A
higher absorbance (K), normalized to the effective path length, by (cos h)1, is indicated for the 473-nm radiation and the
cross-polarized (Kcr) configuration, (c) Kco is found to be proportional to sin2 h.
i.e., Eco 0 = Eco sin h was considered [13] and the transmitted
intensity (which is proportional to Kco) related to the square
0
of the electric field, through |Eco |2. The value of the Kco at
co
h = 0 [K (0)] gave the absorbance for the cross-polarized
configuration while through extrapolating the measured
absorbance to h = 90, i.e., Kco (h = 90), the absorbance for
co-polarized radiation was noted. The corresponding values,
for both 473 and 633 nm wavelengths, are listed in Table 1.
It was then inferred, for example, that at 473 nm, the nanotube absorption for co-polarized radiation was 900 times (related to exp[KcoKcr] = exp[14.98.1] = e6.8) larger than in the
cross-polarized case. While reflectance could be an issue, it is
more important at larger angles. Consequently, we have used
small incidence angles (<40) for our measurements and analyses (e.g., see Fig. 2c, where only the linear part of the graph
has been used). We have estimated a maximum reflectance
Table 1 – Absorbance (K), at 473 and 633 nm for copolarized [Kco (90)], and cross-polarized [Kcr (0)] incident
radiation.
k (nm)
Absorbance
co
K
473
633
(90) =
14.9
11.7
K0k
Kco (0) = K0?
8.1
6.1
of <6% for co-polarized light and a reflectance of <10% for
cross-polarized light [16].
With a perfectly aligned nanotube mat, the absorption
cross-sections r, for either the parallel (r||) or perpendicular
(r?) radiation configuration, could be derived through
K|| = nr||t and K? = nr?t, respectively, given a known CNT density, n, and t. However, such an assumption was unrealistic as
we observed through scanning electron microscopy (SEM)
observations (Fig. 1a) that the synthesized MWCNTs were
not exactly vertical to the substrate, but have a range of
orientations.
3.2.
Influence of the degree of alignment of MWCNT on
transmitted intensity
The transmitted intensity, I, is a function of both (i) polarization angle, a, and (ii) the overall alignment of the CNTs. For
(i), I(a) = I0 sin2a, where a was the angle between the radiation polarization direction and the nanotube axis. The electric field (E) of the incident radiation on a MWCNT is
described through E = E|| + E? (E|| = ~i |E| cos(a) and E? = ~j |E|
sin(a) and where I0 = |E|2. Since it was previously determined
(Section 3.1) that the absorption of the co-polarized radiation
was orders of magnititude larger than the cross-polarized
radiation, the total transmitted electric field was expected to
be close to E?, i.e., E E?. With a perfectly aligned CNT
sample it was then expected that I(0) = I(180) = 0, with
CARBON
minimum transmission (related to E?) while I(90)[=I(270)] is
related to maximum transmission.
As previously outlined, the co- and cross-polarized absorbances, K|| and K? are strictly defined for perfectly oriented
nanotubes, i.e., hui ¼ 0 where u is the polar angle between
the nanotube axis and substrate normal as defined in
Fig. 3a. For a more disordered orientation, i.e., hui–0, the degree of CNT alignment should be considered. Consequently,
the absorbance (K) would be modified to, say K0k and K0? , for
the co- and cross-polarized case, respectively.
To model the CNT misalignment, we assumed a statistical
Gauss–Boltzmann distribution P(u) [17], of the type:
2
PðuÞ ¼ R 1
1
2901
4 7 ( 20 0 9 ) 2 8 9 8–29 0 3
expðA sin uÞ
2
expðA sin uÞdðsin uÞ
P(u) has a maximum probability at u = 0, as shown in Fig. 3a.
A is a parameter, which tends to infinity for perfectly aligned
CNT mats and can be used to characterize alignment. The
parameter A was then determined to be 80 for our particular
MWNT ensemble by comparing the measured transmitted
intensity to a simulated intensity, and was obtained by convoluting P(u) at various values of A with hIðaÞi (Fig. 3b).
3.3.
Order parameter and modified optical absorption
cross-sections
Having determined the appropriate P(u) we determined an order parameter [12,18] S, (0 < S < 1) defined through:
R1
S ¼ 1 PðuÞð3 cos2 u 12Þdðcos uÞ. S = 0 corresponds to a completely random/isotropically aligned CNT ensemble while
S = 1 corresponds to perfect vertical alignment. We then estimated, from the above expression, an S 0.82. The effect of
such a finite S would be to modify the cross-sections, from
r|| and r? to g|| and g?, respectively. Consequently, we express
g|| = a S + b, and g? = c S + d, with the constraint that the net
sum, g|| + 2Æg? is a constant (a, b, c, and d, are constants) which
follows from the consideration that such a sum which is characteristic of an isotropic/unaligned sample is unchanged
from one sample to another [12]. The modified cross-sections
(g|| and g?) were then derived from the measured absorbance
K0
K0
(K0k and K0? ) (see Table 1), i.e., through gk ¼ ntk and g? ¼ nt? .
The CNT density, n, was estimated to be 1.1 · 103 mol/
cm3 – assuming 20 nm diameter MWNTs arranged 200 nm
apart through the SEM observations made on samples shown
in Fig. 1a.
The true absorption cross-sections (r|| and r?) were then calculated from the following equations [12]:
2
1
gk ¼ ðrk r? ÞS þ ðrk þ 2r? Þ
3
3
1
1
g? ¼ ðrk r? ÞS þ ðrk þ 2r? Þ
3
3
These values along with the degree of linear polarization
r r
(DLP) = rkk þr?? , are listed in Table 2. The values previously obtained [13] for SWCNTs were also tabulated for comparison.
It was noted that the optical absorption cross-sections of the
multi-walled CNTs were an order of magnitude larger than
those of SWCNTs. However, the DLP is approximately 35%
smaller.
3.4.
Relationship of the degree of linear polarization to
nanotube diameter
As the absorption cross-sections and the DLP seem to be related to the nanotube diameter (e.g., DLPSWCNT > DLPMWCNT,
as in Table 2), it would be of interest to understand such
dependencies in more detail. For this purpose, we measured
the absorbance (Kco and Kcr) of MWCNTs of different diame-
Table 2 – The co- (r||) and cross- (r?) polarized absorption
cross-sections and the degree of linear polarization (DLP)
for MWCNTs and SWCNTs.
Nanotube Wavelength r|| (Å2/atom) r? (Å2/atom) DLP
(nm)
MWCNT
473
633
0.117
0.098
0.062
0.047
0.31
0.35
SWCNT
473
633
0.029
0.025
0.007
0.005
0.60
0.65
Fig. 3 – (a) The distribution/degree of alignment (through the angle u) of the synthesized MWCNTs was modeled to follow a
Gauss–Boltzmann type distribution, P(u). (b) The variation of the experimentally measured transmitted intensity with the
angle of polarization, a, is in excellent agreement with the simulated intensity obtained by convoluting P(u) (with an A 80)
with the expected transmission.
2902
CARBON
4 7 ( 2 0 0 9 ) 2 8 9 8 –2 9 0 3
Fig. 4 – (a) The absorbance ratio (Kco/Kcr) increases proportionately with the MWCNT diameter (d). The straight lines are a guide
to the eye. (b) The degree of linear polarization (DLP) and the absorption cross-section anisotropy (r||/r?) as a function of the
nanotube diameter.
ters (d 5, 20, and 32 nm) grown from catalyst (Fe) films of
different thicknesses (1.2, 2.8, and 5.5 nm, respectively).
Fig. 4a, indicates, as was previously observed, that the absorbance anisotropy (=Kco/Kcr) varies with sin2 h (c.f., Fig. 2c) and
decreases with increasing catalyst film thickness/nanotube
diameter. The DLP and the absorption cross-section anisotropy (=r||/r?) exhibit a similar trend (Fig. 4b).
While the correlation between the optical absorption and
tube diameter of CNT has not yet been resolved [19], the effects of the depolarization electric field (Ed) were used to give
a qualitative interpretation of the correlation between
absorption cross-section anisotropy (r||/r?) and the tube
diameter (d). For cross-polarized radiation, the depolarization
effect was relaxed as tube diameter increases (i.e., Ed 1/d),
due to a reduced local charge density resulting in r? increasing with an increase in d through r? 1/Ed d. On the other
hand, this depolarization effect does not occur for co-polarized
radiation as the electric field/polarization is now parallel to
the long axis of the CNT, which leads to r|| independent of
Ed. The absorption cross-section (r||/r? Ed 1/d) was then
derived to be inversely proportional to d. Since a MWCNT
can be thought of as being composed of many SWCNTs arranged coaxially would be easy to attribute r|| of a MWCNT
to the summation of those of the constituent SWCNTs, leading to r|| increasing with d. However, if a MWCNT is considered metallic [20], the r|| of a MWCNT would then only be
due to the external layer due to screening effects [21]. Such
correlation could be supported by a previous study on the
thermal properties of MWCNTs [22], which indicated weak inter-wall coupling in MWCNT.
4.
Conclusions
In summary, we have quantitatively determined, for the first
time, the absorption cross-sections for co-polarized (light
polarization parallel to the nanotube axis) and cross-polarized
(light polarization perpendicular to the nanotube axis) radiation for multi-walled CNTs. In the experimental measurements, the orientation and misalignment of the nanotubes
was also considered. It was seen that the measured crosssections (0.1 Å2/atom) are much larger than those previously
determined for single-walled CNTs. Additionally, the co-polarized cross-section is larger by a factor of two compared to the
cross-polarized absorption cross-section. However, the degree
of linear polarization (DLP) was seen to be smaller for the
MWCNT ensembles. The reduction of the depolarization
electric field perpendicular to the CNTs with increasing
diameter and the consequent increased absorption could
be responsible for the reduced DLP. These results indicate
that while MWCNTs are inferior nanoscale polarizing elements, their increased absorption cross-sections could be
utilized for applications involving radiation detection and
absorption.
Acknowledgements
We gratefully acknowledge support from the National Science
Foundation (Grants ECS-05-08514 and DMI-0304019) and the
Office of Naval Research (Award Number N00014-06-1-0234).
R E F E R E N C E S
[1] Bandaru PR. Electrical properties and applications of carbon
nanotube structures. J Nanosci Nanotechnol 2007;7:1239–67.
[2] Chen J, Perebeinos V, Freitag M, Tsang J, Fu Q, Liu J, et al.
Bright infrared emission from electrically induced excitons in
carbon nanotubes. Science 2005;310:1171–4.
[3] Freitag M, Martin Y, Misewich JA, Martel R, Avouris P.
Photoconductivity of single carbon nanotubes. Nano Lett
2003;3:1067–71.
[4] Yang Z, Ci L, Bur A, Lin S, Ajayan P. Experimental observation
of an extremely dark material made by a low-density
nanotube array. Nano Lett 2008;8:446–51.
[5] Taft E, Philipp H. Optical properties of graphite. Phys Rev B
1965;138:197–202.
[6] Longe P, Bose S. Collective excitations in metallic graphene
tubules. Phys Rev B 1993;48:18239–43.
[7] Treacy MMJ, Ebbesen TW, Gibson JM. Exceptionally high
Young’s modulus observed for individual carbon nanotubes.
Nature 1996;381:678–80.
[8] Zhou X, Park J-Y, Huang S, Liu J, McEuen PL. Band structure,
phonon scattering, and the performance limit of single-
CARBON
[9]
[10]
[11]
[12]
[13]
[14]
4 7 ( 20 0 9 ) 2 8 9 8–29 0 3
walled carbon nanotube transistors. Phys Rev Lett
2005;95:146805-1–4.
Kim P, Shi L, Majumdar A, McEuen PL. Thermal transport
measurements of individual multiwalled nanotubes. Phys
Rev Lett 2001;87:215502-1–4.
Theocharous E, Deshpande R, Dillon A, Lehman L. Evaluation
of a pyroelectric detector with a carbon multiwalled
nanotube black coating in the infrared. Appl Opt
2006;45:1093–7.
Shoji S, Suzuki H, Zaccaria R, Sekkat Z, Kawata S. Optical
polarizer made of uniaxially aligned short single-wall carbon
nanotubes embedded in a polymer film. Phys Rev B
2008;77:153407-1–4.
Islam MF, Milkie DE, Kane CL, Yodh AG, Kikkawa JM. Direct
measurement of the polarized optical absorption cross
section of single-wall carbon nanotubes. Phys Rev Lett
2004;93(3):037404-1–4.
Murakami Y, Einarsson E, Edamura T, Maruyama S.
Polarization dependent optical absorption properties of
single-walled carbon nanotubes and methodology for the
evaluation of their morphology. Carbon 2005;43:2664–76.
Aijiki H, Ando T. Aharanov–Bohm effect in carbon nanotubes.
Physica B (Amsterdam) 1994;201:349–52.
2903
[15] Reed B, Sarikaya M. Electronic properties of carbon
nanotubes by transmission electron energy-loss
spectroscopy. Phys Rev B 2001;64:195404-1–13.
[16] Saleh BEA, Teich MC. Fundamentals of photonics. 2nd
ed. Hoboken, NJ: John Wiley and Sons; 2007.
[17] Fujiwara M. Magnetic orientation and magnetic properties of
a single carbon nanotube. J Phys Chem A 2001;105(18):
4383.
[18] Chaikin PM, Lubensky TC. Principles of condensed matter
physics. New York: Cambridge University Press; 1995.
[19] Jost O, Gorbunov A, Pompe W, Pichler T, Friedlein R, Knupfer
M, et al. Diameter grouping in bulk samples of single-walled
carbon nanotubes from optical absorption spectroscopy.
Appl Phys Lett 1999;75:2217–9.
[20] Martel R, Schmidt T, Shea HR, Hertel T, Avouris P. Single- and
multi-wall carbon nanotube field-effect transistors. Appl
Phys Lett 1998;73:2447–9.
[21] Ando Y, Zhao X, Shimoyama H, Sakai G, Kaneto K. Physical
properties of multiwalled carbon nanotubes. Int J Inorg Mater
1999;1:77–82.
[22] Yi W, Lu L, Zhang DL, Pan ZW, Xie SS. Linear specific heat of
carbon nanotubes. Phys Rev B 1999;59:R9015–8.